不确定车轨耦合系统辛随机振动分析

SYMPLECTIC RANDOM VIBRATION ANALYSIS FOR COUPLED VEHICLE-TRACK SYSTEMS WITH PARAMETER UNCERTAINTIES

建立了轨道不平顺作用下具有不确定参数车轨耦合系统随机振动评估方法.车辆系统采用物理坐标下多刚体系统模型,并应用高斯随机变量模拟车体、转向架和轮对一系、二系连接系统中动力学参数具有的不确定性.采用无穷周期结构进行弹性轨道模拟,在哈密顿状态空间下建立了典型轨道子结构的状态运动方程,通过轮轨耦合关系建立了混合物理坐标及辛模态坐标车轨耦合系统运动方程.应用Hermite正交多项式展开得到了耦合系统动力响应相对于不确定性参数的控制方程.由于利用轨道周期特性建模,所获得的控制方程有效地降低了方程维度.轮轨接触处轨道不平顺载荷模拟为完全相干多分量平稳随机过程,推广和发展虚拟激励法建立了耦合系统随机振动受不确定动力学参数影响的量化评估方法.通过Monte Carlo数值模拟,验证了该方法在不确定参数变异很大时也能够保持较好的精度,具有一定的工程实用性.

A new random vibration-based assessment method for coupled vehicle-track system with uncertain parameters subjected to random track irregularity is proposed in this paper. The vehicle system is simplified as a spring-mass-damper system model by using physical coordinates, and the uncertainties in the primary suspension and secondary suspension for the body, bogies and wheels are modeled by Gaussian random ＇variables. The track is treated as a Bernoulli-Euler beam connected to sleepers and the ballast and is regarded as an infinite periodic structure. The state equation for a typical sub-structure of the track is established in the Hamiltonian system. The dynamic equations of the coupled vehicle-track system under the mixed physical coordinates and symplectic dual coordinates are established based on the wheel-rail coupling relations. The control equation with respect to the uncertain parameters is derived by using the Hermitian orthogonal polynomials for dynamic analysis of the coupled systems. By using the periodic features of the track, the ＂curse of dimensionality＂ of the control equation is effectively reduced. The wheel-rail contact forces due to the track irregularity are assumed to be fully coherent stationary random processes. An assessment of the random vibration with respect to the uncertain parameters is established for the coupled vehicle-track system by using the pseudo-excitation method （PEM）. The proposed method is compared with the Monte Carlo simulations, and it is found that good agreements are achieved even for cases with strong uncertainties in system parameters.